The Ruin Problem Of Sparre-Andersen Model With The Geometric Distributionof Claim Inter-Occurrence Times For Insurance

In this paper,we consider a Sparre Andersen risk model with geometric distribution of claim inter-occurrence times.The claim size distribution can be a general discrete distribution. This risk process is made into a homogeneous piecewise deterministic Markov process by introducing supplementary components from forward Markovization technique. Then a martingale is found by the martingale approach of piecewise deterministic Markov process(PDMP). The general expression and the Lundberg bound of the ruin probability are derived subsequently.The idea of change of the probability measure and the adjustment coefficient are used to find the Lundberg bound.This paper includes Three chapters.Several elementary concepts of PDMP and the extended generator of PDMP are introduced in the first chapter.The classical risk model and the Sparre Andersen model are introduced in the second one.The third chapter is the main body of this paper in which the ruin problem of Sparre Andersen model with geometric distribution of claim inter-occurrence times is considered and the Lundberg bound is derived .